# Consecutive Integers Word Problems Worksheet

## 6 problems

Consecutive integer word problems involve solving math problems related to numbers that follow one another without gaps. To solve these problems, we set up an equation by examining the rules and characteristics of consecutive integers to find the value of the missing numbers. In these worksheets, students will first set up an equation using the properties of consecutive integers and then, will find the value of the integers.

For example: There are 3 consecutive integers that add up to 27. Which integers are they?

Algebra 1
One-Variable Equations

## How Will This Worksheet on "Consecutive Integers Word Problems" Benefit Your Students' Learning?

• Enhances problem-solving abilities and fosters critical thinking skills.
• Helps to develop a better understanding of algebraic concepts such as linear equations, variables, and expressions.
• Encourages thinking in order and understanding the progression from one number to the next.
• Develops skills in logical reasoning,...
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## Solved Example

Q. There are $3$ consecutive integers with a sum of $54$. What are the integers?$\newline$$\_$, $\_$, $\_$
Solution:
1. Define Consecutive Integers: Let $x$ be the first integer. The three consecutive integers can be represented as $x$, $x+1$, and $x+2$.
2. Set Up Equation: Set up the equation to represent the sum of the three consecutive integers equal to $54$.$\newline$Equation: $x + (x+1) + (x+2) = 54$
3. Simplify Equation: Simplify the equation by combining like terms.$\newline$$x + x + x + 1 + 2 = 54$$\newline$$3x + 3 = 54$
4. Isolate Variable Term: Isolate the variable term by subtracting $3$ from both sides of the equation.$\newline$$3x + 3 - 3 = 54 - 3$$\newline$$3x = 51$
5. Solve for x: Solve for x by dividing both sides of the equation by $3$.$\newline$$\frac{3x}{3} = \frac{51}{3}$$\newline$$x = 17$
6. Find Consecutive Integers: Find the three consecutive integers using the value of $x$.$\newline$First integer: $x = 17$$\newline$Second integer: $x + 1 = 17 + 1 = 18$$\newline$Third integer: $x + 2 = 17 + 2 = 19$

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